Hello, New here and just looking this site over. I am the owner of a 04 Limited with the same problem. The Heater Treater solution looks decent. I'm looking to go with the dual control through the glove box. Check it out http://heatertreater.net

Could be the blend doors. A common fault that Chrysler I believe are aware of, something to do with poor welding I think. I have heard of replacement kits that are a type of upgrade. Then again it could well be the heater core matrix. May not leak for a few days, so there may not be any obvious signs, other than cold air blowing out. Either way can be an expensive fix as someone rightly said, the dashboard has to come off

OK guy when the blend doors are bad now there are more then a hand full of option to fix it compared to 5 years ago.

instead of having to take out the dash and spend all day doing it or paying a shop or dealer over $800 theirs a simle fix if your blend door/doors are broken. just have to cut a hole behind the dash and can replace the doors with stronger metal doors

dont go to a junk yard and buy the same plastic doors that will brake again

more info0 on it:
a company called heatertreater has a dual control fix but you have to add a bigger motor and cut part of your glove box so it looks odd. but they cam up with the first fix of making the dual control single control, which helps people.

also now Chrysler has a new version of the doors which they say is stronger and people that have had then installed have been doing well with them. also teh dealer now used this threw teh dash fix.

if you have a bad core have to re move the dash and when its out change all the parts (core, doors, rec door) since they will go at some point.

there is a simple fix that can cost a person under a buck to fix the rec door. you just proper it up so its open all the time, will not get ride of the code but will still have it functioning. some people drill a hole in the door and tie wrap it open. other get a coat hanger and bend/cut it to the right then to keep the door open then hold the metal on the dash with a screw.